The Effects of Financial Aid on First-Time 
College Attendance Decisions




Haining Cheng
and
Miles Bryant
University of Nebraska
(March, 1997)










A Research Paper Presented at the Association for Institutional 
Research 37th Annual Forum, May 18-21, 1997, Lake Buena Vista, Florida



Running Head: Theoretical Model






Abstract

	This paper examined the effects of financial aid in various forms on first time attendance decisions at a Midwestern land-grant university.  Patterned after a model for assessing the effects of student aid on first time attendance by St. John (1992), a logistic regression model was reconceptualized and tested using existing data.  
	The researchers argue that university and higher education policy makers need to understand better financial aid as an effective strategy for improving the probability that students will elect to enroll.  This paper models that decision event.  
	The results of the test indicate that logistic regression is a workable model and may be applied in any institutional setting.  Grants and loans were found significantly and positively associated with an increased probability of attendance; work study was found to have a significant negative probable relationship with attendance.  








INTRODUCTION

	The financing of public higher education in America has traditionally relied on government provided subsidies to keep tuition low and to maintain access.  This was one of the principles of the land-grant legislation (Hearn & Longanecker, 1985).  In recent years all forms of public financing of higher education have come under closer scrutiny (Lewis, 1989).  One of the main financial issues has centered about the efficiency of student financial aid as a means of ensuring access to higher education.
	The role of financial aid programs in promoting access to higher education has been a primary focus of a number of education policy researchers (Corman & Davidson, 1984; Hearn, 1988; Jackson, 1978; James, 1988; St. John & Noell, 1989; St. John, 1991, 1992; Tierney, 1980).  After decades of government financial support to students in higher education, there is still substantial controversy about the effectiveness of financial aid in promoting access (Hansen, 1983; Hanson, 1991; James, 1988; Orfield, 1992; Schwarts, 1985).  While research with national data bases usually confirms that financial aid has a positive influence on student attendance and persistence (Astin, 1975; Terkla, 1985, Leslie & Brinkman, 1988; St. John & Noell, 1989; St. John et al., 1991, St. John, 1990a, 1990b, 1991; St. John et al., 1994), there remains controversy over the degree to which financial aid affects attendance when examined at the institutional level (St. John, 1992).  Studies assessing the impact of financial aid have often produced inconsistent results on the role of aid in influencing college attendance (Hearn, 1988; James, 1988; Moore et al., 1991; Schwartz, 1985; Seneca & Taussig, 1987). 
	There are a number of reasons underlying these inconsistent results.  First, the study of financial aid and its impacts must factor in complex political, economic, and social variables.  It is not always possible to identify and operationalize such variables.  Second, inconsistent logical models and statistical methods have been used (St. John, 1992).  Third, different research methods using different data bases have led to different results (Hopkins, 1974; Knudsen & Servelle, 1978; McPherson & Shapiro, 1991; Moore, et al., 1991; Parker & Summrs, 1993).  Fourth, research has not been conducted in diverse institutional settings; thus generalizations of financial aid models across different types of institutional settings has been limited.  As a result, the question of whether financial aid is uniformly effective in promoting access remains unsettled (McPherson & Shapiro, 1991; Orfield, 1992).  The role of student financial aid in positively impacting college student attendance merits further investigation.
	The purpose of this study was to reconceptualize and test a logistic regression model proposed by St. John (1992) for institutional research in assessing the effects of financial aid on first-time attendance decisions in a Research I land-grant university setting.

RESEARCH APPROACH
	
	Grounding his explorations in three domains, the economic theory on student demand, the sociological research on educational attainment, and the policy research on student choice, St. John (1992) proposed logistic regression as a means of modeling the impact of financial aid on college student attendance decisions.  This model viewed first-time attendance as a dichotomous variable--either applicants attended or they did not.  Decisions by accepted college applicant to attend were expressed as a function of three factors: social background, academic preparation, and student financial aid.  Each factor was comprised of a set of related variables. To test the model, St. John proposed the use of logistic regression, a statistical technique that accommodates dichotomous variables.
	Our study followed St. John's design and viewed first time college student attendance decisions as a function of the three major factors: social background, academic preparation, and student financial aid.  The outcome variable was student attendance, a dichotomous variable (enrolled or did not enroll),.  Since the goal of this analysis was to obtain a single overall estimate of the effect of an exposure variable (attendance decision) adjusted for other factors such as the independent variables in the model, the main effect logistic regression model was appropriate.  Conceptually, the model was defined as:

A = f (SB, AP, FA)

where 		A = first time attendance, SB = social background, 
		AP = academic preparation, FA = financial aid in various forms.
	The independent variables related to each factors are presented below:
	1) Social background factors:
		Gender (Females coded as 0)
		Age (Treated as continuous variable)
		Ethnicity (Whites coded as 0; all others coded as 1)
		Dependency Status (Independents coded as 0)
		Family Income (dummy-coded to create two new variables: below $15,000 coded 
			as 1; $15,001-30,000 coded as 1; above $30,000 treated as reference group 
			and coded as 0)
	2) Academic Preparation
		ACT scores (dummy-coded to create two new variables: 1-17 coded as 1; 18-26
			coded as 1; 27-36 treated as reference group and coded as 0)
		High School Rank (dummy-coded to create two new variables: below 50% coded 
			as 1; 50% to 75% coded as 1; above 75% treated as reference group and 
			coded as 0)
	3) Financial Aid
		Any aid (Aid recipient coded as 1; no aid coded as 0)
		Total amount of aid (coded on scale of $1,000 increments; e.g.
			1=$1,000)
		Types of Aid (Each coded by type on scale of $1,000 increments; e.g.
			1=$1,000)
		Aid Packages (Grand only, loan only, work study only, grant and loan, grant and 
			work study, loan and work study, grant and loan and work study-receipt 
			of each type coded as 1)
	
Database
	This study used an institutional data base as a source.  The analysis considered accepted applicants since this was the only population that could be directly influenced by institutional aid awards.  There were 5,363 first time applicants who were accepted into the undergraduate program in the fall of 1995.  A data set was created from two files: financial aid files and admissions office files.  The former provided information about social background factors (family income, dependency status) and financial aid (any aid, amount of aid, types of aid).  The admissions office provided the remaining necessary data.  To better represent the general characteristics of the population, only applicants who were American citizens were selected.  Furthermore, only students who provided information on family income were included, an exclusion factor that reduced the usable cases to 2,638.

Methodology
	The focus of this study was to test a logistic regression model.  A sequential logistic regression technique was employed as the major means of statistical assessment.  Logistic regression was selected because it is an appropriate for a model containing dichotomous variables (Austin et al., In Smart, 1992; Cabrera et al., In Smart, 1994; Kleinbaum, 1994; St. John, 1992; Wright in Grimm & Yarnold, 1995).  This type of statistical research has been considered a powerful procedure when used appropriately (Morgan & Teacyman, 1988).  St. John (1990, 1991) and St. John and Associates (1989, 1991, 1994) have used this technique in their national research on attendance and persistence.  
	The logit form of the model in mathematical expression was defined as:
									 
	l	logit P (x) = ( + ( (i Xi		where	

	Four versions of logistic regression were developed, tested, and analyzed.  The first version examined the impact of receiving any aid on the attendance decision.  The second version examined the impact of the amount of aid in dollars on attendance.  The third version examined the impact of receiving three different types of aid on attendance.  And the fourth examined the impact of six types of financial aid packages on attendance.
	Three steps were undertaken for the sequential regression analysis.  First, we analyzed the effect of social background variables on attendance.  Second, we included the added effect of academic preparation.  Third, we added financial aid factors while controlling for the first two sets of variables.  As noted by St. John (1991), the use of sequential logistic regression makes it possible to test for the added effect that different groups of independent variables have on the probability of an outcome.

Logistic Regression
	Assessing a logistic regression model is not as straightforward as assessing a linear regression model.  In the later, tests and measures of goodness of fit are widely known and used.  Since there is no universal agreement as yet on the statistical measures that should be used to assess the quality of the logistic regression model best, we used several different approaches.  First, we used a somewhat known approach called the likelihood ratio test which is a chi -square statistic using-2 LL.  This measure allows one to assess how well the estimated model fits the data (Wright in Grimm & Yarold, 1995).  Smaller -2 Log L values indicate better fitting models.  
	Because some researchers have argued that the maximum likelihood function per se has little value in judging whether or not the model is a valid one (Calrera in Smart, 1994), we used three additional measures to evaluate our models: 1) the Pseudo R2, which is characterized as "in the spirit of R2 (Aldrich & Nelson, 1984); 2) the proportion of cases correctly predicted (PCP), which provides an overall indicator of fit (Aldrich & Nelson, 1984); and 3) the G2/df ratio , which is another indicator of how well the model fits the data (Cabrera et al, In Smart, 1994).  These three measures combined can provided a reasonable indication of how well the model works.  We also used the Wald test to determine the significance of individual coefficients.  Each of these model statistics is presented in Tables 1-4.
	In addition to assessing the performance of the model, logistic regression produces regression coefficients that must be interpreted.  We used two statistics to capture the effect of independent variables on dependent variable.  The first statistic we used was the Odds Ratio (OR) which estimates the change in the odds of membership (as opposed to non-membership) in a target group for every unit increase in a predictor variable (Kleinbaum, 1994).  In our study, for example, if the Odds Ratio were 5.5, it would mean that the odds of a student enrolling were 5.5 times greater for a student receiving financial aid than for a student receiving none.  The second statistic, the Delta p statistic, was used for each variable with a significant coefficient using a formula recommended by Peterson (1984).  The reason for using the Delta p statistic was that the beta value for logistic regression could be converted into probability measures which were easier to conceptualize and understand.  The Delta p statistic has been used by St. John (1990a, 1990b, 1991) and St. John and Associates (1989, 1991, 1994) in their national financial aid research.  The Delta p statistic was defined as follows:

		Delta p = exp (L1) / [1+exp (L1)] - exp (L0) / [1+exp (L0)]

		Where L0 = Ln p / (1-p) 	(p = "baseline p" in tables); 	L1 = L0 + beta

	It should be noted that the Delta P statistic provides a measure of the change in probability associated with one unit change in the measure used for a particular independent variable (St. John, 1992).  For example, if the significant coefficient for a grant in aid were .05, it would mean that this type of aid increased the probability of the student enrolling by 5 percentage points.  Thus, for each $1,000 increase in grant money, the probability of the student attending would increase by 5 percentage points.
	
FINDINGS

	First we indicate how well our model performed generally.  Second, we present the four analytical models we constructed of the impact of financial aid on the attendance decision.
	In all four versions of our model, the addition of variables at each of the three steps increased the ability of the model to predict attendance.  This was indicated by the reduction in the -2LL statistic in each step across all four versions of the model (see Tables 1-4).  This change in -2LL between successive steps of building the model was mirrored by the statistic labeled Model Improvement.  Note (in Tables 1-4) that only when the third step is completed does the Model Improvement statistic become significant.  Note also that "pseudo R2" also increases at each stage of analysis, especially with the addition of the financial aid variables.  Next, the overall percentage of cases correctly classified (PCP) by each respective version of the model was 56.4 (Table 1); 53.7% (Table 2); 56.6% (Table 3); and 58.6% (Table 4).  Last, the G2/df ratio statistics were 1.31 (Table 1); 1.38 (Table 2); 1.37 (Table 3); and 1.30 (Table 4), all less than the value of 2.5 recommended by Stage (1990) as the minimum value necessary in order to accept the model.  Taken together, these measures indicate that our model performs adequately.  We also note that the fourth version of the model (Table 4) was our best fitting one.
	We followed the same analytical pattern in each of our four versions of the model.  In our first step we examined social background (gender, ethnicity, age, dependence, income); in our second, we examined academic factors (ACT scores and class rank); and in our third, financial aid.  Unless indicated, all statistics reported are significant at the .05 level.
	Analysis One
	We first sought to know to what degree the offer of any financial aid increased the probability of attendance in our sample.  In this model, the odds of enrolling were about 6 times greater (OR = 5.907) for a student who received an offer of financial aid.  The Delta p statistic reflects the same pattern.  The offer of financial aid increased the probability of a student's enrolling by about 40% (Delta p = 39.6).  Neither social background nor academic variables had significant impact on the probability of a student enrolling and the model's predictive efficacy emerged only when the financial aid factor was added.

					Table 1 About Here

The data in Table 1 indicate that social background and academic preparation variables were statistically insignificant and appeared not to increase the probability of attendance.  This result is surprising in view of prior financial aid studies which have found that family income and minority ethnicity were significant predictors of attendance (St. John & Noell, 1989; St. John, 1990, 1991, 1992).  
	Analysis Two
	In our second version of the model, we sought to evaluate the effect of a unit increase in the dollar amount of financial aid on the attendance decision.  In this analysis we found that the odds of enrolling were about 1.1 times greater for each student who received a $1,000 increase in aid (OR = 1.06) and that each $1,000 in aid increased the probability of attendance by 2% (Delta P = .02).  

					Table 2 about here

As in our first analysis, social background and academic variables were not significant contributors to the robustness of the model.
	Analysis Three
	In our third version of the model, we explored the effects of three different types of financial aid measured in dollars: 1) grants, 2) loans, and 3) work study.  We found that the odds of enrolling increased 1.1 times for each $1,000 dollar increase in grant money (OR = 1.1).  A $1,000 increase in grant money increased the probability of attendance by about 2% (delta p = .02).  The odds of enrollment were increased by 1.13 times (OR = 1.13) for each $1,000 in loan money; each $1,000 increase in loans were accompanied by an 3% climb in the probability of attendance 3% (delta p = .03). 

					Table 3 about here

 Interestingly, a $1,000 increase in work study led to a decline in the odds of enrollment (OR = .77).  An OR of less than 1.0 is a negative.  Each $1,000 increase in work study decreased the probability of attendance by 6% (Delta p = .06).
	Analysis Four
	The fourth version of the model looked at different aids packages: 1) grants only, 2) loans only, 3) grants and loans, 4) grant and work, 5) loan and work, and 6) grant, loan, and work.  In the second and third versions above we measured aid in terms of dollars.  Here we made use of the particular properties of logistic regression and used the type of financial aid expressed as a nominal variable.  

					Table 4 about here

We found that four types of variables had a positive impact on enrollment.  Grants only increased the odds of enrollment 5 times (OR = 4.6).  The probability of enrollment was increased by 36% (delta p = .36).  Loans increased the odds of enrollment by almost 6 times (OR = 5.5) and the probability of enrollment by 39% (delta p = .39).  When grants and loans were combined, the increase in the odds of enrolling went up 7 times (OR = 7.2) and the probability of enrolling increased 43% (delta p = .43).  Grants, loans, and work study combined yielded an odds ratio of 5.0 (OR = 5.0) and an increase in the probability of attendance of 37% (delta p = .37).  Because work study was negatively related to the enrollment decision, its effect was to depress the increase in probability.  The other two types of financial aid combinations (Grant and Work and Loan and Work) had no significant impact on the enrollment decision.

DISCUSSION AND CONCLUSION

	Our first interest was in applying and testing the use of logistic regression to analyze the decision of the applicant.  We found that in general logistic regression is a workable technique for institutional financial aid research.  Even using a limited number of variables (our model is probably overly parsimonious), we were able to calculate the impact of different forms of financial aid on the enrollment decisions.  However, there are problems with our model.  First, as in all social science research utilizing the predictive modeling of complex human behavior, it is impossible to construct a mathematical model that includes all relevant variables.  For example, we are unable to calculate the influence of competitor institutions on the enrollment decisions of the students in our study.  Perhaps, even though a student was offered financial aid at our institution, that student may have gotten a better deal elsewhere.  We were unable to measure this effect.  Nor were we able to measure family income accurately.  We were able to get family income from two sources (ACT Reports and Financial Aid Applications) but these two sources were not compatible.  Furthermore, not all students indicated family income on their ACT reports.  Thus, this important variable was not measured as well as we would have liked.
	Our study did lead findings that warrant continued investigation and continued use of logistic regression as a tool for policy analysis.  
	We found that grants and loans did have a significant and positive impact on the student enrollment decision and that we could calculate the impact that increasing amounts of financial aid produced.  As the model is refined to produce more accurate predictions of the applicant response, this kind of information promises to be useful to university and college administrators as they develop financial aid strategies to influence potential students.  
	We found that social background and academic preparation variables were not significant predictors and played remarkably small roles in attendance.  This result is inconsistent with some prior financial aid studies which have found that family income and minority ethnicity were significant predictors of attendance (St. John & Noell, 1989; St. John, 1990, 1991, 1992).  
	We found that students responded differently to different types of aid.  Grant, loan, and grant and loan combination were more effective than other types of aid awards.  This finding supports the findings from several recent national aid studies (e.g. St. John, 1990, 1991; St. John & Starkey, 1995).
	We also found that work study decreased the probability of attendance.  When we explored this finding, we learned that at the institution in our study a ceiling or limit is placed on the amount of work study money that can be offered a student.  This ceiling is quite low.  Thus, work study is not seen as particularly attractive to many students since they can earn more working off campus.  St. John (1992) found a similar result in his national study.  In our study students appeared to prefer loans to work study.  Perhaps greater amounts of money budgeted for work study might alter this tendency.  The effectiveness of work study as a strategy is one that each institution should evaluate.
	As the costs of attending higher education escalate, the importance of financial aid increases.  Finding the means to allocate financial aid more efficiently is necessary if college and universities are to maximize this strategy for impacting the enrollment decision.  Logistic regression and the model we have presented offer a means whereby administrators may explore the utility of their financial aid strategies. 
	

















REFERENCES

Astin, Alexander W. (1975).  Preventing Students from Dropping Out.  San Francisco:  Jossey-Bass.

Aldrich, J. H. & Nelson, F. D. (1984).  Linear Probability, Logit and Probit Models.  Beverly Hills, CA:  Sage Publications.

Andrieu, Sandra (1991).  The Influence of Background, Graduate Experience, Aspirations, Expected Earnings and Financial Commitment on Within-Year Persistence in Graduate Programs.  University of New Orleans: Unpublished Doctoral Dissertation.

Austin, James T., Yaffee, Robert A., and Hinkle, Dennis (1992).  Logistic regression for research in higher education.  In Smart, John C (ed.).  Higher Education:  Handbook of Theory and Research, Vol. VIII. New York: Agathor Press.

Bryman, Alan & Cramer, Duncan (1990).  Quantitative Data Analysis for Social Scientists. Routledge, London.

Cabrera, A., Nora, A. & Castaneda, M. (1992).  The role of finances in the persistence process: a structural model.  Research in Higher Education, Vol. 33, No. 5, pp. 571-593

Cabrera, Alberto F. (1994).  Logistic regression analysis in higher education: an applied perspective.  In Smart, John C. (ed.).  Higher Education: Handbook of Theory and Research, Vol.X, New York: Agathon Press.

Corman, Hope, & Davidson, Patricia (1984).  Economic aspects of post-secondary schooling decisions.  Economics of Education Review, Vol. 3, No. 2 pp. 131-139.

Fife, J. D. (1975).  The College Student Grant Study.  Center for the Study of Higher education: The Pennsylvania State University. 

Hansen, W. (1983).  Impact of Student Financial Aid on Access.  In Froomkin, Joseph (ed.).  The Crisis in Higher Education.  New York: Academe of Political Science.

Hanson, Janet S.(1991).  The Roots of Federal Student Aid Policy.  In New Directions for Higher Education, No. 74, summer, pp. 3-18.

Hearn, James & Longanecker, David (1985).  Enrollment Effects of Alternative 
Postsecondary Pricing Policies.  Journal of Higher Education, Vol. 56, No.5 
(September/October).

Hearn, James (1988).  Attendance at higher-cost colleges: ascribed, socioeconomic, and academic influences on student enrollment patterns.  Economics of Education Review, Vol. 7, No. 1, pp. 65-76.

Hopkins, T. (1974).  Higher education enrollment demand.  Econ. Inquiry.  Vol. 12, pp. 53-65.
Jackson, Gregory (1978).  Financial aid and student enrollment.  Journal of Higher Education, Vol. 49, No. 6, pp. 548-574.

James, Estelle (1988).  Student aid and college attendance: Where are we now and where do we go from here?  Economics of Education Review, Vol. 7, No. 1, pp. 1-13.

Kleinbaum, David G. (1994).  Logistic Regression: A Self-Learning Text.  Springer-Verlay, NY. Inc.

Knudson, O. & Servelle, P (1978).  The demand for higher education at private institutions of moderate selectivity.  American Economics.  Vol. 16. pp. 30-34.

Leslie, L. L. & Brinkman, P.T. (1988).  The Economic Value of Higher Education.  New York: Macmillan.

Lewis, G. L. (1989).  Trends in student aid: 1962-63 to 1988-89.  Research in Higher Education, 30(6), pp. 547-562.

McPherson, Michael and Schapiro, Morton Owen (1991).  Does student aid affect college enrollment?  New Evidence on A Persistent Controversy.  American Economic Review.  81, pp. 309-318.

Moore, R. L., Studenmund, A. H. & Slobko, T. (1991).  The effect of the financial aid package on the choice of a selective college.  Economics of Education Review.  Vol. 10, No. 4, pp. 311-321.

Orfield, Gary (1992).  Money, equity, and college access.  Harvard Educational Review,  Vol. 62, No.3, Fall.  pp.337-369

Parker, Jeffrey & Summers, Jefffey (1993).  Tuition and enrollment yield at selective liberal artscolleges.  Economics of Education Review, Vol. 12, No. 4, pp. 311-324.

Paulsen, Michael B. (1990).  College Choice: Understanding Student Enrollment Behavior.  ASHE-ERIC Higher Education Reports.  Clearinghouse on Higher Education: The George Washington University.

Peterson, Trond (1984).  A comment on presenting results from logit and probit models.  American Sociological Review.  Vol. 50 (1),  pp.130-131.

Schwarts, Brad (1985).  Student financial aid and the college enrollment decision: the effects of public and private grants and interest subsidies.  Economics of Education Review. Vol. 4, No. 2. pp. 129-144.

Seneca, Joseph J. & Taussig, Michael K. (1987).  The effects of tuition and financial aid 	on the enrollment decision at a state university.  Research in Higher Education.  Vol. 26, No. 4. pp. 337-362.

St. John, Edward & Noell, Jay (1989).  The impact of student aid on access to higher education: an analysis of progress with special consideration of minority enrollment.  Research in Higher Education, 30(6): pp. 563-581.

St. John, Edward (1990a).  Price response in enrollment decisions: An analysis of the high school and beyond sophomore cohort.  Research in Higher Education, Vol. 31, No. 2, PP. 161-176.

St. John, Edward (1990b).  Price response in persistence decisions: An analysis of the high school and beyond senior cohort.  Research in Higher Education, Vol. 31, No. 4,  pp.387-403.

St. John, Edward, Krishstein, Rita & Noell, Jay (1991).  The effects of student financial aid on persistence: A sequential analysis.  The Review of Higher Education.  Spring, Vol. 14, No. 3, pp. 383-406.

St. John, Edward (1991).  What really influences minority attendance?  Sequential analysis of the high school and beyond sophomore cohort.  Research in Higher Education, Vol. 32, No. 2, pp. 141-158.

St. John, Edward (1992).  Workable models for institutional research on the impact of student aid.  Journal of Student Financial Aid.  22(3), pp. 13-26.

St. John, Edward, Andrieu, Sandra, Oescher, Jeffrey, and Starkey, Johnny (1994).  The influence of student aid on within-year persistence by traditional college-age students in four-year colleges.  Research in Higher Education, Vol. 35, No. 4, pp. 455-480.

St. John, Edward & Starkey, Johnny (1995).  An alternative to net price: Assessing the influence of prices and subsidies on within-year persistence.  Journal of Higher Education, Vol. 66, No. 2, pp. 156-186.

Stage, F. K. (1990).  LISREL: An introduction and applications in higher education.  In J.C. Smart (ed.).  Higher Education: Handbook of Theory and Research, Vol. VI. New York: Agathon Press.

Terkla, Dawn G (1985).  Does financial aid enhance undergraduate persistence?  Journal of Student Financial Aid.  Vol. 15, No. 3 (Fall), pp. 11-18.

Tierney, Michael (1980).  Student matriculation decisions and student aid.  Review of Higher Education, Vol. 3, pp. 14-25.

Wright, Raymond E. (1995).  Logistic Regression.  In Grimm, Laurence G. and Yarnold, Paul R. (eds.).  Reading and Understanding Multivariate Statistics.  Washington, DC.

16
								Theoretical Model

15
								Theoretical Model